Trapezoidal footing is a type of footing that holds unequal loads from 2 columns when the heaviest load outside the column distance is restricted.

It is utilized when the area of footing is fixed and the soils at the site are loose soil.

### 1. Formula for Calculating Trapezoidal Footing Volume

As we know, Trapezoidal footing is made by the superimposing of a rectangular cuboid and truncated pyramid as shown in the figure below.

Now,

The volume of trapezoidal footing=Volume of Rectangular cuboid (V1)  +  Volume of a truncated pyramid (V2)

= V1 + V2       …………….(Eq.1)

I. Volume of rectangular cuboid (V1);

= A * B * hc    …………….(Eq.2 )

where,

A= length of the cuboid

hc= Height of cuboid

II. Volume of a truncated pyramid ( V2 );

= ht/3 * ( A1 + A2 + √(A1 +A2) )  ……..(eq.3)

Where,

A1= area of the bottom surface of the truncated pyramid

A2= area of the upper surface of the pyramid

ht= height of the pyramid

From equations 1,2 and 3, we can write the final  formula for calculating the volume of  trapezoidal footing as shown below;

= V1 + V2

= ( A*B*hc)  + ht/ 3 ( A1 + A2 + (√ (A1+A2)) )

Now, We are going to find out the volume of trapezoidal footing shown in Figure 3 above;

i. ht= 300mm = 0.3m

ii. hc= 300mm=0.3m (let us assume)

iii. Area of cuboid (A *B)= (2000 mm * 1600 mm) = 3.2 m²

iv. Area of the bottom surface of the pyramid(A1) =3.2m²

v. Area of the top surface of the pyramid (A2)= (800*800) mm2 =0.64m²

Now,

Total Volume= V1 + V2

=( A*B*hc)  + ht/ 3 ( A1 + A2 + (√ (A1+A2)) )

=(3.2 * 0.3) + 0.3/3 (3.2+0.64 +(√(3.2+0.64)))

=0.96 +0.57995

= 1.539959 m3

The total volume of the trapezoidal footing in figure 3 = 1.5399m3

### 3. Uses

Trapezoidal footing’s uses are as follows:

I. For residential houses and buildings.

II. When the load applied is uneven or unequal.

III. The soil at the site is loose.

The advantages of trapezoidal footing are as follows:

a. Concrete uses are less.

b. Cheap to construct.

c. Less reinforcement is needed.

The disadvantages of trapezoidal footing are as follows:

a. Good for small buildings only.

b. Chance of settlement.

c. Foundation subjected to pull out, torsion, moment.

### 6. References

1. Content Filter & Authenticity Checking Team, Dream Civil International

(Our team checks every content & detail to maintain quality.)

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